I spend time each year in Puerto Vallarta, Mexico. Aside from the consistently wonderful weather, one of the differences I've noticed is the traffic. There are very few traffic signals and stop signs. Interestingly, there are also very few traffic accidents. You pull up to a busy intersection and, since nothing dictates what you should do, you pay attention to the other cars. There's no red light to stop at or jump, nor stop sign at which to stop or fake a stop. You simply do what the moment dictates.
Often we don't speed to avoid a ticket or the loss of our license. Similarly, many people don't cheat or steal for fear of getting caught. If we had Plato or Frodo's ring to make us invisible, what would we do? Sadly, I think a large number of us would misbehave if we knew that we could get away with it. There's research showing that children are more likely to cheat when exams have proctors than when the honor system is in place. Instead of subtle incentives that encourage us to beat the system, what would happen if there were no system to beat?
What would happen if children early on were taught the consequences of their actions on others, rather than to behave well in order to avoid punishment? What if they were trusted to do the right thing rather than threatened. Imagine these lessons continuing into adulthood. Certainly this might make a difference for reasonably minor transgressions. My belief, though, is that even more serious infractions might also diminish and morality would take the place of the necessity for many of the laws now on the books.